Floored

A floor is covered by a tessellation of equilateral triangles, each having three equal arcs inside it. What proportion of the area of the tessellation is shaded?

Pie Cuts

Investigate the different ways of cutting a perfectly circular pie into equal pieces using exactly 3 cuts. The cuts have to be along chords of the circle (which might be diameters).

Getting an Angle

How can you make an angle of 60 degrees by folding a sheet of paper twice?

Integral Polygons

Stage: 3 Short Challenge Level:
The greatest number of sides the polygon could have is $360$.

As each interior angle of the polygon is a whole number of degrees, the same must apply to each exterior angle. The sum of the exterior angles of a polygon is $360^{\circ}$ and so the greatest number of sides will be that of $360$-sided polygon in which each interior angle is $179^{\circ}$, thus making each exterior angle $1^{\circ}$.

This problem is taken from the UKMT Mathematical Challenges.
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